10.6 Polar Coordinates

Polar Coordinates are only half as scary as the name sounds. No, it's not like the "Polar Vortex" or the "Polar Express", it is instead a method of describing distance and direction using a radius and an angle.

In a standard (X,Y) grid, points are based upon distance X and distance Y, in a polar grid, none of that applies, and points are based upon the hypotenuse of (X,Y) and the angle the line forms with the horizontal.

The hypotenuse is easy to find, just use the Pythagorean Theorem! The square root of (X^2)+(Y^2)

is the first part of a polar coordinate, the radius (r).

The second part of the polar coordinate is the degree measure that the coordinate is based upon the measurement the hypotenuse of (X,Y) forms with the horizontal, using a right triangle, we can determine that this is arcsin(Y/X). This gives us the degree measure for a Polar Coordinate, Theta.

Congratulations! You may now know how to convert between Rectangular Coordinates and Polar Coordinates, you should celebrate with cake or other delicious pastries.